hmmm theres figures out there somewhere, for anything but time trials and maybe tri its a pretty trivial saving. having spoken to people runing them though, the superficial difference is meant to be very noticable (ie smoothness of BBs and wheels.)
aah while that is right dumbellina, what he said wasnt really anything to do with instantaneous kinetic energy,
It is kinetic energy - the potential energy (chemical) in the muscles leading to muscle extension/contraction (kinetic), which is transmitted through the pedals to the cranks, into the chain, into the rear wheel, which is then transmitted to the road. The wheel exerts a force on the road, the road applies an opposite and equal force on the bike (and rider), and because of the mass differential the bike move forward, accelerating and increasing velocity (which means their kinetic energy is increased).
The amount of energy used to move forward and increase your velocity is the same, the gears merely mechanical advantage by increasing the torque you are applying on the rear wheel.
Torque (rotational force) = force x distance (from the centre of rotation)
In respect of bike gears - distance is based on the ratio of teeth on the front sprocket and the rear sprocket - or in simple terms the distance one rotation of the chainring causes the rear cluster to rotate. See bike mechanic books that usually have a table of torque "distances" in "gear inches" if from the US.
The energy savings purported in the new pedalling method regarded the efficiency losses in the transmission of energy from cranks to chain. But the "engineer type" was right in saying that the efficiency gains over the standard crank set-up were uncertain.
The old shimano biometric chainrings still used by George Hindcappie (the only one to still use them) offered to increase the efficiency in the same aspect of energy transmission at the "flat spot in the pedal stroke. Other designs allege to offer similar efficiency gains.
But the inventor didn't even say how his invention improved on those anti "flat" spot devices, or that this was the efficiency that he was seeking to gain.
An inventor with an invention that may work, many electrical inventions such as Thomas Edison's many inventions, but no real "benefit" was provided or proven.